A281532 a(n) = least numerator X such that the proper fraction X/A281529(n) needs n or more terms to be written as a signed sum of distinct unit fractions.

1, 2, 5, 18, 118

Offset: 1

Author

Arkadiusz Wesolowski, Jan 23 2017

Keywords

• nonn
• frac
• hard
• more

Comments

Sierpiński conjectured that for any integer n > 3 there exist positive integers a, b, c so that 5/n = 1/a + 1/b + 1/c. If the conjecture is true, then 5 appears only once in the sequence.

References

• W. Sierpiński, O rozkładach liczb wymiernych na ułamki proste, PWN, Warsaw, Poland, 1957, pp. 96-100.

Crossrefs

See A281529 for denominators.